Upon reading the bpp text, I got the impression that the centered average is calculated over an even number of periods(eg 4 quarters) as in your lecture.However, an example in the text shows a 12 month period where the centered average was not calculated.The moving average was used to represent the trend .I have difficulty understanding this.
If it is an even number then the average should be centred to get the trend.
I only have the BPP Revision Kit (not their Study Text) and so I can’t check their question/answer, but if what you have typed is correct then they are wrong to call it the trend without having centred it.